A common procedure for measuring the electrical conductivity comprises placing two electrodes in a solution, supplying electricity to the solution through the electrodes, measuring the voltage U across the ends of the electrodes and measuring the current I flowing there between. The resistivity of the solution is determined by calculating the resistance R between the two electrodes according to the expression R=U·I−1. Further, the conductivity G of the solution is given by the expression G=C·R−1, where C is the electrode constant and R is the resistance between the electrodes. The conductivity is the reciprocal of the resistivity of the solution.
However, uniformly directed current between the electrodes in the solution will also decompose (i.e., polarize) the solution and thereby produce an electromotive counter force. The counter force, known as the effect of polarization, decreases the current flow or involves higher exiting voltages and consequently introduces a dynamically changing measurement error. Consequently the measured resistance of the solution will drift with time. A common way to address the measurement error caused by this polarization is to use an alternating current for the measurement.
For an ideally short connecting cable arranged between the electrodes and the measurement circuit the measurement accuracy will rise with an increasing current frequency. However, this does not hold for practical connecting cables since there always exists a certain cable capacitance, which leads to an increased error at higher frequencies. Therefore, reducing the cable length and increasing the frequency of the current are two ways to increase the accuracy of the measurements, but these parameters can also interfere with each other.
CN1619318 A discloses a method, in which the electrodes are excited by sine signals of two different frequencies. As a result, a modulus |Za| and |Zb| for each of the two impedances Za and Zb is obtained, as well as the ratio r=|Za|·|Za|−1. The electrical conductivity G of the solution can then be calculated according to the expression:
  G  =            K              -        1              ·          (                                              Z            a                                    ·                              1            +                                                            r                  2                                -                1                                            4                -                                  r                  2                                                                        )      with K being the cell constant and r being the ratio of the two impedances Za and Zb. The disclosed method addresses only the effect of polarization: But this method does not address (e.g., eliminate) the effect of the electrode polarization as well as the effect of a long cable simultaneously.
CN1459629 discloses a method for performing a measurement based on a concept of usable power. By measuring the voltage and the current of a solution, the expression:
  G  =      C    ·                  ∫                              I            2                    ⁢                      ⅆ            t                                      ∫                              U            ·            I                    ⁢                      ⅆ            t                              is applied to obtain the electrical conductivity G of the solution. This method addresses the effect of polarization but again, this method does not address (e.g., eliminate) both effects.
DE 4 233 110 A1 discloses a method for determining an exciting frequency. A base frequency and an adjacent frequency, which differs about 20% from the base frequency, is used to conduct two measurements. If the difference between the results of these measurements is small, the used base frequency is considered to be right; otherwise the base frequency will be changed and new measurements will be conducted. This can be repeated until optimal frequencies are found, and the error can be estimated. Nevertheless, this method is a known single frequency method.
U.S. Pat. No. 6,369,579 B1 discloses a method to reduce the error in a determination of the conductivity of a solution with a measurement converter and an alternating voltage at two frequency values. The method and the equivalent circuit diagram consider the effects within the measurement cell, but not the cable capacitance. The disclosed solution is not suitable in cases with long connecting cables.
In general, for an actual measurement setup, both the capacitance of the cable and the polarization of the electrode exist simultaneously, regardless of the used frequency, Therefore, the known methods do not address (e.g., eliminate) errors arising from both effects simultaneously.